1. Statement of the Technical Field
The invention concerns communication systems. More particularly, the invention concerns permission-based time division multiple access (TDMA) chaotic communication systems.
2. Description of the Related Art
Multiple access communication systems permit multiple users to re-use a portion of a shared transmission spectrum for simultaneous communications. Multiple access communications may be implemented using frequency diversity, spatial diversity (with directional antennas), time diversity, or coding diversity. The most common method of employing time diversity in a multiple access communication system is with time division multiple access (TDMA), where multiple users have designated timeslots within a coordinated communications period called a frame or epoch in which to transmit their information. In some cases, the frame is of such short duration that users transmitting low data rates (e.g., voice communication signals) appear to receive continuous service. Numerous variations to the basic TDMA communications approach exist, with increased performance of a communications waveform or protocol translating to more users or more efficient use of the communications spectrum. Most often, the scheduling of epochs and timeslots is chosen as a deterministic process. The most common method of coding diversity, as often applied to code division multiple access communication systems, is the use of statistically orthogonal (or, more simply, orthogonal) spreading codes that can be used to differentiate between two or more signals. The phrase “statistically orthogonal spreading codes”, as used herein, refers to spreading codes whose inner product over a finite duration has a statistical expectation of zero.
Pseudorandom number generators (PRNG) generally utilize digital logic or a digital computer and one or more algorithms to generate a sequence of numbers. While the output of conventional PRNG may approximate some of the properties of random numbers, they are not truly random. For example, the output of a PRNG has cyclostationary features that can be identified by analytical processes.
Chaotic systems can generally be thought of as systems which vary unpredictably unless all of its properties are known. When measured or observed, chaotic systems do not reveal any discernible regularity or order. Chaotic systems are distinguished by a sensitive dependence on a set of initial conditions and by having an evolution through time and space that appears to be quite random. However, despite its “random” appearance, chaos is a deterministic evolution.
Practically speaking, chaotic signals are extracted from chaotic systems and have random-like, non-periodic properties that are generated deterministically and are distinguishable from pseudo-random signals generated using conventional PRNG devices. In general, a chaotic sequence is one in which the sequence is empirically indistinguishable from true randomness absent some knowledge regarding the algorithm which is generating the chaos.
Some have proposed the use of multiple pseudo-random number generators to generate a digital chaotic-like sequence. However, such systems only produce more complex pseudo-random number sequences that possess all pseudo-random artifacts and no chaotic properties. While certain polynomials can generate chaotic behavior, it is commonly held that arithmetic required to generate chaotic number sequences digitally requires an impractical implementation due to the precisions required.
Communications systems utilizing chaotic sequences offer promise for being the basis of a next generation of low probability of intercept (LPI) waveforms, low probability of detection (LPD) waveforms, and secure waveforms. Chaotic waveforms also have an impulsive autocorrelation and a compact power spectrum, which make them ideal for use in a multiple access communication system. While many such communications systems have been developed for generating chaotically modulated waveforms, such communications systems suffer from low throughput. The term “throughput”, as used herein, refers to the amount of data transmitted over a data link during a specific amount of time. This throughput limitation stems from the fact that a chaotic signal is produced by means of a chaotic analog circuit subject to drift.
The throughput limitation with chaos based communication systems can be traced to the way in which chaos generators have been implemented. Chaos generators have been conventionally constructed using analog chaotic circuits. The reason for reliance on analog circuits for this task has been the widely held conventional belief that efficient digital generation of chaos is impossible. Notwithstanding the apparent necessity of using analog type chaos generators, that approach has not been without problems. For example, analog chaos generator circuits are known to drift over time. The term “drift”, as used herein, refers to a slow long term variation in one or more parameters of a circuit. The problem with such analog circuits is that the inherent drift forces the requirement that state information must be constantly transferred over a communication channel to keep a transmitter and receiver synchronized.
The transmitter and receiver in coherent chaos based communication systems are synchronized by exchanging state information over a data link. Such a synchronization process offers diminishing returns because state information must be exchanged more often between the transmitter and the receiver to obtain a high data rate. This high data rate results in a faster relative drift. In effect, state information must be exchanged at an increased rate between the transmitter and receiver to counteract the faster relative drift. Although some analog chaotic communications systems employ a relatively efficient synchronization process, these chaotic communications systems still suffer from low throughput.
In particular, time division communication systems employing chaotic signals are especially sensitive to chaotic state uncertainties since a receiver not continuously synchronized to a transmitter requires additional computational effort to re-acquire the chaotic signal during each of its assigned communication bursts. The drift that occurs between assigned timeslots limits the flexibility of applying time division multiple access (TDMA) communications protocols using a chaotic physical layer signal. Permission-based timeslot scheduling algorithms, as commonly used in TDMA communications protocols, is an additional complexity that is currently not supported by communications with a chaotic signal since the generation of orthogonal communication signals using chaotic signals requires extreme flexibility in the determination of initial chaotic state parameters.
The alternative to date has been to implement non-coherent chaotic waveforms. However, non-coherent chaotic waveform based communication systems suffer from reduced throughput, error rate performance and exploitability. In this context, the phrase “non-coherent waveform” means that the receiver is not required to reproduce a synchronized copy of the chaotic signals that have been generated in the transmitter. The phrase “communications using a coherent waveform” means that the receiver is required to reproduce a synchronized copy of the chaotic signals that have been generated in the transmitter.
In view of the forgoing, there is a need for a coherent chaos-based communications system having an increased throughput. There is also a need for a chaos-based communications system configured for generating a signal having chaotic properties. There is further a need for a chaos-based time division multiple access communication system.